After solving each system, 5x + y = 0, 5x + 2y = 30, the values of x and y are calculated to be -6 and 30 respectively.
The given equations are considered linear equations as the highest power of the variables in these equations is one.
By rearranging the first equation, the value of y can be found to be,
5x + y = 0
y = -5x
Putting the calculated value of y in the second equation,
5x + 2y = 30
5x + 2(-5x) = 30
5x - 10x = 30
-5x = 30
x = 30 / -5
x = -6
To solve for y, put x = -6 in the first equation as follows,
5x + y = 0
5(-6) + y = 0
-30 + y = 0
y = 30
Hence, the values of x and y in these systems are calculated to be -6 and 30 respectively.
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